Interaction-Induced Quasicrystalline Order: Emergence of Quasi-Solid and Quasi-Supersolid Phases

Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(παi)\cos(παj), where n=α=sqrt{5}-1/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.